There are some black and purple marbles in a container. If 3 black marbles are removed from the container, the total number of marbles left will be 9 times the number of black marbles left. If 60 purple marbles are removed from the container, the total number of marbles left will be 3 times the number of black marbles. How many marbles are there in the container?

	Case 1		Case 2
	Black marbles	Purple marbles	Black marbles	Purple marbles
Before	1 u + 3	8 u	1 p	2 p + 60
Change	- 3			- 60
After	1 u	8 u	1 p	2 p

Number of purple marbles in the end for Case 1
= 9 u - 1 u
= 8 u

Number of black marbles in the end for Case 2
= 3 p - 1 p
= 2 p

The number of black marbles at first is the same for Case 1 and Case 2.
The number of purple marbles at first is also the same for Case 1 and Case 2.

1 u + 3 = 1 p --- (1)

8 u = 2 p + 60
8 u - 60 = 2 p --- (2)

Make p the same.

(1)_x2
2 u + 6 = 2 p --- (3)

(2) = (3)
8 u - 60 = 2 u + 6
8 u - 2 u = 6 + 60
6 u = 66

1 u = 66 ÷ 6 = 11

Number of marbles in the container
= (1 u + 3) + 8 u
= 9 u + 3
= (9 x 11) + 3
= 99 + 3
= 102

Answer(s): 102